A building under construction is seen amidst smog on a polluted day in Shenyang, Liaoning province in this November 21, 2014 file photo. REUTERS/Jacky Chen/Files

BENGALURU/NEW YORK (Reuters) - The global economy finished last year on a fragile footing, with factory activity in China shrinking for the 10th month running in December, while euro zone manufacturing picked up but U.S. activity slowed.

Coming on a day of volatility in Asian stock markets after China’s central bank fixed the yuan at a 4-1/2 year low, the data point to sluggish economic growth and inflation globally to start the new year.

European stock markets fell too, though the declines were less sharp as investors took note of the brighter data from the euro zone. At midsession, U.S. stocks were down nearly 3.0 percent, the biggest one day fall in more than three months.

CHINA FACTORY ACTIVITY CONTRACTS

The Caixin/Markit China Manufacturing Purchasing Managers’ Index (PMI) slipped to 48.2, below a Reuters poll consensus of 49.0 and down from 48.6 in November.

That was the lowest since September and well below the 50-point level that separates contraction from expansion. It followed a fractional increase in the official PMI to 49.7.

The PMIs in South Korea and Taiwan edged above the 50 mark, though more thanks to a pick-up in domestic demand than any revival in exports.

Weighed down by weak demand at home and abroad, factory overcapacity and cooling investment, China will likely post its weakest economic growth in 25 years in 2015, with the rate of expansion slipping to around 7.0 percent from 7.3 percent in 2014.

Growth is forecast to slow to 6.5 percent this year and next, according to the latest Reuters poll.

The drag from industry comes as China makes gradual progress in its transformation to a more service-driven economy. An official survey on the services sector showed activity quickened in December, with its main index rising to 54.4, from 53.6 in November.

China has room to ease reserve requirements for banks and loosen government purse strings. It has also been steadily nudging its currency lower.

EURO ZONE MANUFACTURING EXPANDS

Manufacturing activity in the euro zone area improved last month in all the countries covered by the business survey from private data vendor Markit, suggesting factories performed better over last year as a whole compared to the previous three.

A worker drives a forklift to transport aluminum bars at a factory in Anshun, Guizhou province, China, July 1, 2013. REUTERS/Stringer

Markit’s final manufacturing Purchasing Managers’ Index (PMI) rose to a 20-month high of 53.2, just above a flash reading of 53.1 and of 52.8 in November. The PMIs suggest a pickup in activity, but in most countries still a mild pace of growth.

This year “is going to be a rerun of 2015 with added risks,” said Peter Dixon, economist at Commerzbank. “The global economic story is based on weak fundamentals with China slowing further and policy uncertainties existing in developed economies.”

While the PMIs point to improving activity in the euro zone, the European Central Bank would have to expand its policy arsenal to get inflation back up to its target, he added.

The ECB has already cut its deposit interest rate well below zero and is buying 60 billion euros a month of mostly government bonds to try and boost inflation. Price pressures are still subdued in the region, but a December Reuters poll suggests market expectations of bigger asset purchase program also remain low.

Data on Tuesday is expected to show euro zone inflation rose to 0.3 percent in December from 0.2 percent in November.

A regional bright spot was Italy, where manufacturing activity grew at its fastest pace in almost five years, auguring well for growth in the euro zone’s third-largest economy.

British factory growth slipped however as new orders came in at the slowest pace in five months.

U.S. FACTORY ACTIVITY SLUMPS

U.S. manufacturing activity slowed further in December, as the impact of a stronger U.S. dollar undermined export profitability.

Markit’s purchasing managers’ index (PMI) fell to 51.2 from 52.8 in November, the lowest since October 2012.

The new orders subcomponent fell to 50.2 from 53.1, the lowest since Sept 2009.

“A near-stagnation in new business volumes was the main factor weighing on the headline index in December,” Markit’s U.S. economist Tim Moore said.

“Export sales were also close to stagnation in December, with manufacturers noting that the strong dollar continued to act as a drag on demand from abroad.”

An alternative reading from the U.S. Institute for Supply Management (ISM) said its index of national factory activity fell to 48.2 from 48.6 in November and is now at its lowest level since June 2009.

Additional reporting by Jonathan Cable and Andy Bruce in LONDON, Isla Binnie in ROME, Dan Burns in NEW YORK; editing by John Stonestreet and Clive McKeef